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P(x)= Q(x)S(x), P(x) Q(x) , P(x) Q(x) , S(x),
P(x)= Q(x)S(x), , P(x) Q(x). P(x), Q(x), S(x) , , . , P(x) Q(x). , .
P(x) Q(x) P(x) P(x)= Q(x)S(x)+ R(x), R(x) , R(x) Q(x). .
- P(x) Q(x) S(x) R(x), P(x)= Q(x)S(x)+ R(x).
ij . .
1. P(x)= x3 1 Q(x)= x + 1. .
x3 1 = (x + 1)(x2 x + 1) 2. S(x)= x2 x + 1, R(x)= - 2.
2. P(x)= x4 +4x3 4x2 + x + 1 Q(x)= x2 +2x + 1. .
: x4 + 4x3 4x2 + x + 1 = (x2 +2x + 1)(x2 + 2x 9) +17 x + 10.
x4 +4x3 4x2 + x + 1 = (x2 +2x + 1)(ax2 + bx + c) + dx + e
x4 +4x3 4x2 + x + 1 = ax4 +(2a + b)x3 +(c + 2b + a)x2 +(b + d + 2c)x + e + c
.
x4 + 4x3 4x2 + x + 1 = (x2 +2x + 1)(x2 + 2x 9) +17 x + 10
.
P(x) = a 0xn + a 1xn-1 ++ a n-1x + a n; Q(x) = x ; S(x) = b 0xn-1 + b 1xn-2 ++ b n-1.
a 0xn + a 1xn-1 + + a n-1x + a n = (x )(b 0xn-1 + b 1xn-2 + + b n-1) + R (1.7)
R R x . S(x) Q(x)
a 0xn + a 1xn-1 + + a n-1x + a n = b 0xn + (b 1 - c b 0 )xn-1 + +(bn -1 - c bn -2 )x + R - c bn -1 (1.8)
b 0 = a 0; bk = cbk-1 + ak (k = 1, 2, 3,, n), bn = R. R= bn-1 + an (1.9)
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1.4
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P(x) = a 0xn + a 1xn-1 + + a n-1x + a n (1.10)
, . . P(x) = x2 + 9 , x2 + 9 = (x + 3i)(x 3i). i = - . P(x)
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P(x) = a 0(x x1)(x x2)(x xn). (1.11)
, , :
a 0xn + a 1xn-1 + + a n-1x + a n = a 0(xn (x1 + x2 + + xn)xn-1 + (1.12)
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1.5
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P(x)=P(x0)+(x-x0)P(x0,x1)+(x-x0)(x-x1)P(x0,x1,x2)++ (1.18)
(x-x0)(x-x1)(x-xn)P(x0,x1,,xn);
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RESUME